I'm in the same boat. As well as this, I've rebooted my computer (no small feat, it takes upwards of 10 minutes because it's quite crappy) and it fixes nothing.
ON TOP OF THIS, my client has a bug that has caused the entire launch window to be zoomed in, meaning the rightmost content of the launcher is actually inaccessible, and therefore I can't even repair the client. The only thing I can think of is a hard re-install, which is garbage because I just did that 3 days ago to fix an unrelated problem. But now I've tried to join an ARAM, missed out on the entire game, and can't create a custom game either. Now that the custom is ongoing, I can't even quit it because when I try to Reconnect, it does exactly what you say: Minimizes but takes me nowhere.
Riot, this is silly. Fix it.